The renormalized Φ44 trajectory by perturbation theory in the running coupling (I). The discrete renormalization group Original Research Article

We compute the renormalized trajectory of massless Φ4 theory on four-dimensional Euclidean space-time by perturbation theory in a running coupling. We introduce an iterative scheme without reference to a bare action. The renormalized Φ4 trajectory is described as an invariant curve in the center manifold of the trivial fixed point, tangent to the Φ4 interaction. The expansion is proven to be finite to every order of perturbation theory. The proof includes a large momentum bound on the connected momentum space Green functions.